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The nonlinear temporal evolution of a disturbance to a stratified mixing layer

Published online by Cambridge University Press:  26 April 2006

Roland Mallier
Roland Mallier
Affiliation:
Department of Mathematics, McGill University, Montreal, PQ, H3A 2K6, Canada
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Abstract

Using a nonlinear critical layer analysis, Goldstein & Leib (1988) derived a set of nonlinear evolution equations governing the spatial growth of a two-dimensional instability wave on a homogeneous incompressible tanh y mixing layer. In this study, we extend this analysis to the temporal growth of the García model of an incompressible stratified shear layer. We consider the stage of the evolution in which the growth first becomes nonlinear, with the nonlinearity appearing inside the critical layer. The Reynolds number is assumed to be just large enough so that the unsteady, nonlinear and viscous terms all enter at the same order of magnitude inside the critical layer. The equations are solved numerically for the inviscid case.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 291 , 25 May 1995 , pp. 287 - 297
Copyright
© 1995 Cambridge University Press

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